Identify networks from longitudinal data: homogeneous vs heterogeneous model

# number of nodes
p=40
# number of edge in general network
m1=70
# the difference between the number of edges in individual networks and general network
m2=20
# number of subjects
n=60

One-stage model

Estimate the network based on homogeneous one-stage model

Generate data


set.seed(1)
dd=Simulate(type="longihomo",n=n,p=p,m1=m1,m2=m2,tau=2,tt=10)
ddata=dd$data
subjects=fct_inorder(ddata$subject)
group=rep(0,nrow(ddata))
homoData=list(data=ddata)
#saveRDS(homoData,file="homoOneStageData.rds")

Estimation

set.seed(1)
aa=lglasso(data=ddata,lambda = 0.01,trace=T)
#> [1] "iteration 1 precision difference: 3.648 /correlation tau difference: 0.133"
#> [1] "iteration 2 precision difference: 1.936 /correlation tau difference: 1.589"
#> [1] "iteration 3 precision difference: 1.753 /correlation tau difference: 1.405"
#> [1] "iteration 4 precision difference: 1.212 /correlation tau difference: 1.271"
#> [1] "iteration 5 precision difference: 1.183 /correlation tau difference: 0.978"
#> [1] "iteration 6 precision difference: 0.756 /correlation tau difference: 0.942"
#> [1] "iteration 7 precision difference: 0.738 /correlation tau difference: 0.567"
#> [1] "iteration 8 precision difference: 0.368 /correlation tau difference: 0.557"
#> [1] "iteration 9 precision difference: 0.363 /correlation tau difference: 0.25"
#> [1] "iteration 10 precision difference: 0.14 /correlation tau difference: 0.247"
#> [1] "iteration 11 precision difference: 0.138 /correlation tau difference: 0.089"
#> [1] "iteration 12 precision difference: 0.046 /correlation tau difference: 0.088"
#> [1] "iteration 13 precision difference: 0.046 /correlation tau difference: 0.029"
#> [1] "iteration 14 precision difference: 0.015 /correlation tau difference: 0.029"
#> [1] "iteration 15 precision difference: 0.014 /correlation tau difference: 0.009"
#> [1] "iteration 16 precision difference: 0.005 /correlation tau difference: 0.009"
#saveRDS(aa,file="homoOneStageResult.rds")
## estimated network 
estimates=lapply(aa$wi,function(ll){ifelse(abs(ll)>10^(-3),1,0)})
estimates
#> [[1]]
#>     V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12 V13 V14 V15 V16 V17 V18 V19 V20 V21
#> V1   1  0  0  1  1  0  1  1  0   0   0   0   0   1   1   0   0   0   0   1   1
#> V2   0  1  0  1  1  0  1  0  0   0   1   1   1   0   0   0   0   1   0   1   1
#> V3   0  0  1  1  1  1  1  1  0   0   0   1   0   0   0   0   0   0   1   1   1
#> V4   1  1  1  1  0  0  0  1  1   0   0   0   0   0   0   1   0   1   1   1   0
#> V5   1  1  1  0  1  1  0  0  0   0   0   0   1   0   1   0   1   0   1   0   0
#> V6   0  0  1  0  1  1  1  1  0   1   0   0   0   1   0   1   1   0   0   0   0
#> V7   1  1  1  0  0  1  1  0  1   0   1   0   0   1   0   1   0   0   0   1   1
#> V8   1  0  1  1  0  1  0  1  0   0   1   0   0   0   1   0   0   1   0   0   0
#> V9   0  0  0  1  0  0  1  0  1   1   0   1   1   1   0   0   1   0   0   1   0
#> V10  0  0  0  0  0  1  0  0  1   1   1   0   0   0   0   1   0   0   0   1   0
#> V11  0  1  0  0  0  0  1  1  0   1   1   0   0   0   1   1   0   0   0   1   0
#> V12  0  1  1  0  0  0  0  0  1   0   0   1   1   0   0   0   1   1   0   0   0
#> V13  0  1  0  0  1  0  0  0  1   0   0   1   1   1   0   0   0   1   0   0   1
#> V14  1  0  0  0  0  1  1  0  1   0   0   0   1   1   0   0   0   1   0   0   0
#> V15  1  0  0  0  1  0  0  1  0   0   1   0   0   0   1   0   0   0   0   1   0
#> V16  0  0  0  1  0  1  1  0  0   1   1   0   0   0   0   1   0   0   0   0   0
#> V17  0  0  0  0  1  1  0  0  1   0   0   1   0   0   0   0   1   1   0   0   0
#> V18  0  1  0  1  0  0  0  1  0   0   0   1   1   1   0   0   1   1   1   0   1
#> V19  0  0  1  1  1  0  0  0  0   0   0   0   0   0   0   0   0   1   1   0   0
#> V20  1  1  1  1  0  0  1  0  1   1   1   0   0   0   1   0   0   0   0   1   0
#> V21  1  1  1  0  0  0  1  0  0   0   0   0   1   0   0   0   0   1   0   0   1
#> V22  0  1  0  0  0  0  0  0  1   0   0   1   0   0   0   0   1   0   1   0   1
#> V23  1  0  1  0  1  0  0  1  1   1   1   1   0   1   0   0   1   1   0   0   1
#> V24  1  1  0  1  1  1  1  0  1   1   1   0   1   1   1   0   0   0   1   1   1
#> V25  1  0  1  0  0  0  0  0  0   1   0   0   0   0   0   0   1   0   1   0   0
#> V26  0  1  1  1  1  0  0  0  0   0   1   0   0   0   0   1   0   0   0   0   0
#> V27  0  0  0  0  0  0  1  0  0   0   0   1   0   0   1   0   1   1   0   1   0
#> V28  1  1  1  1  1  1  0  0  0   0   0   1   0   1   1   0   1   1   0   1   1
#> V29  0  1  0  0  0  0  0  0  0   0   0   0   0   0   1   0   0   0   0   1   0
#> V30  1  1  1  0  0  1  0  0  0   1   0   0   1   0   0   0   0   0   0   1   1
#> V31  0  1  1  1  0  1  1  1  1   0   1   1   1   1   1   1   0   0   0   1   1
#> V32  0  0  0  0  0  0  0  0  0   0   0   1   0   1   0   0   0   0   1   1   1
#> V33  1  1  1  0  0  1  0  1  0   0   0   0   0   1   0   1   0   1   1   0   0
#> V34  0  1  1  1  0  0  0  1  1   1   1   1   1   1   1   0   1   0   0   0   1
#> V35  0  1  0  0  1  1  1  0  0   0   1   1   1   0   1   0   0   0   0   0   1
#> V36  1  1  0  1  1  0  1  0  0   0   1   0   0   1   0   0   0   1   1   0   1
#> V37  0  1  1  1  1  0  1  0  0   0   1   0   0   0   0   0   1   1   1   1   0
#> V38  1  0  0  1  0  0  1  1  0   1   0   0   1   1   0   1   1   0   1   0   0
#> V39  1  0  1  1  0  0  0  0  0   0   0   0   0   1   1   0   0   1   1   0   0
#> V40  0  0  0  0  1  0  0  0  0   0   0   1   0   0   0   0   0   0   1   0   0
#>     V22 V23 V24 V25 V26 V27 V28 V29 V30 V31 V32 V33 V34 V35 V36 V37 V38 V39 V40
#> V1    0   1   1   1   0   0   1   0   1   0   0   1   0   0   1   0   1   1   0
#> V2    1   0   1   0   1   0   1   1   1   1   0   1   1   1   1   1   0   0   0
#> V3    0   1   0   1   1   0   1   0   1   1   0   1   1   0   0   1   0   1   0
#> V4    0   0   1   0   1   0   1   0   0   1   0   0   1   0   1   1   1   1   0
#> V5    0   1   1   0   1   0   1   0   0   0   0   0   0   1   1   1   0   0   1
#> V6    0   0   1   0   0   0   1   0   1   1   0   1   0   1   0   0   0   0   0
#> V7    0   0   1   0   0   1   0   0   0   1   0   0   0   1   1   1   1   0   0
#> V8    0   1   0   0   0   0   0   0   0   1   0   1   1   0   0   0   1   0   0
#> V9    1   1   1   0   0   0   0   0   0   1   0   0   1   0   0   0   0   0   0
#> V10   0   1   1   1   0   0   0   0   1   0   0   0   1   0   0   0   1   0   0
#> V11   0   1   1   0   1   0   0   0   0   1   0   0   1   1   1   1   0   0   0
#> V12   1   1   0   0   0   1   1   0   0   1   1   0   1   1   0   0   0   0   1
#> V13   0   0   1   0   0   0   0   0   1   1   0   0   1   1   0   0   1   0   0
#> V14   0   1   1   0   0   0   1   0   0   1   1   1   1   0   1   0   1   1   0
#> V15   0   0   1   0   0   1   1   1   0   1   0   0   1   1   0   0   0   1   0
#> V16   0   0   0   0   1   0   0   0   0   1   0   1   0   0   0   0   1   0   0
#> V17   1   1   0   1   0   1   1   0   0   0   0   0   1   0   0   1   1   0   0
#> V18   0   1   0   0   0   1   1   0   0   0   0   1   0   0   1   1   0   1   0
#> V19   1   0   1   1   0   0   0   0   0   0   1   1   0   0   1   1   1   1   1
#> V20   0   0   1   0   0   1   1   1   1   1   1   0   0   0   0   1   0   0   0
#> V21   1   1   1   0   0   0   1   0   1   1   1   0   1   1   1   0   0   0   0
#> V22   1   1   0   0   1   0   1   0   0   1   0   0   1   0   0   1   1   1   1
#> V23   1   1   1   1   1   0   0   0   1   0   1   1   1   1   1   1   1   1   1
#> V24   0   1   1   1   0   1   1   0   0   1   0   1   0   1   1   1   1   0   0
#> V25   0   1   1   1   0   1   0   0   0   1   1   1   0   1   0   0   1   1   1
#> V26   1   1   0   0   1   0   1   0   0   1   0   0   0   1   0   1   1   1   0
#> V27   0   0   1   1   0   1   1   1   1   1   0   0   0   1   0   0   0   1   0
#> V28   1   0   1   0   1   1   1   1   0   1   0   0   1   1   1   1   1   0   0
#> V29   0   0   0   0   0   1   1   1   1   1   1   0   0   0   1   0   1   1   0
#> V30   0   1   0   0   0   1   0   1   1   1   1   0   0   1   0   1   1   0   1
#> V31   1   0   1   1   1   1   1   1   1   1   0   1   1   1   0   0   0   1   1
#> V32   0   1   0   1   0   0   0   1   1   0   1   0   0   1   0   0   0   1   1
#> V33   0   1   1   1   0   0   0   0   0   1   0   1   0   0   0   0   1   1   0
#> V34   1   1   0   0   0   0   1   0   0   1   0   0   1   1   0   0   0   1   0
#> V35   0   1   1   1   1   1   1   0   1   1   1   0   1   1   0   0   0   1   0
#> V36   0   1   1   0   0   0   1   1   0   0   0   0   0   0   1   0   1   0   0
#> V37   1   1   1   0   1   0   1   0   1   0   0   0   0   0   0   1   1   1   0
#> V38   1   1   1   1   1   0   1   1   1   0   0   1   0   0   1   1   1   1   0
#> V39   1   1   0   1   1   1   0   1   0   1   1   1   1   1   0   1   1   1   1
#> V40   1   1   0   1   0   0   0   0   1   1   1   0   0   0   0   0   0   1   1
## true network 
dd$network
#>     V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12 V13 V14 V15 V16 V17 V18 V19 V20 V21
#> V1   1  0  0  0  0  0  0  0  0   0   0   0   0   0   1   0   0   0   0   0   0
#> V2   0  1  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   1
#> V3   0  0  1  0  0  0  0  0  0   0   0   1   0   0   0   0   0   0   0   0   0
#> V4   0  0  0  1  0  0  0  0  0   0   0   0   0   0   0   1   0   0   0   1   0
#> V5   0  0  0  0  1  0  0  0  0   0   0   0   0   0   0   0   0   0   1   0   0
#> V6   0  0  0  0  0  1  0  1  0   0   0   0   0   0   0   1   0   0   0   0   0
#> V7   0  0  0  0  0  0  1  0  0   0   0   0   0   1   0   1   0   0   0   0   0
#> V8   0  0  0  0  0  1  0  1  0   0   0   0   0   1   1   0   1   0   0   0   0
#> V9   0  0  0  0  0  0  0  0  1   1   0   0   0   1   0   0   1   0   0   0   0
#> V10  0  0  0  0  0  0  0  0  1   1   0   0   0   0   0   1   0   0   0   0   0
#> V11  0  0  0  0  0  0  0  0  0   0   1   0   0   0   0   1   0   0   0   0   0
#> V12  0  0  1  0  0  0  0  0  0   0   0   1   0   0   0   0   0   0   0   0   0
#> V13  0  0  0  0  0  0  0  0  0   0   0   0   1   1   0   0   0   0   1   0   0
#> V14  0  0  0  0  0  0  1  1  1   0   0   0   1   1   0   0   0   1   0   0   0
#> V15  1  0  0  0  0  0  0  1  0   0   0   0   0   0   1   0   0   0   0   0   0
#> V16  0  0  0  1  0  1  1  0  0   1   1   0   0   0   0   1   0   0   0   0   0
#> V17  0  0  0  0  0  0  0  1  1   0   0   0   0   0   0   0   1   0   0   0   0
#> V18  0  0  0  0  0  0  0  0  0   0   0   0   0   1   0   0   0   1   0   0   1
#> V19  0  0  0  0  1  0  0  0  0   0   0   0   1   0   0   0   0   0   1   0   0
#> V20  0  0  0  1  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   1   0
#> V21  0  1  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   1   0   0   1
#> V22  0  0  0  0  0  0  0  0  0   0   0   1   0   0   0   0   0   0   1   0   0
#> V23  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V24  0  0  0  0  0  0  0  1  0   0   0   0   1   0   0   0   0   0   0   0   0
#> V25  1  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V26  0  1  0  0  1  0  0  1  0   0   0   1   0   0   0   1   0   0   0   0   0
#> V27  0  0  0  0  0  0  0  0  0   0   0   0   0   0   1   0   1   0   0   0   0
#> V28  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V29  0  0  0  0  1  0  0  1  0   0   0   0   0   0   1   0   0   0   0   0   0
#> V30  0  0  0  0  0  1  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V31  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V32  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   1   1   0
#> V33  0  0  0  0  0  0  1  0  0   0   0   0   0   0   0   0   0   0   1   1   0
#> V34  0  0  0  0  0  0  0  0  0   0   1   0   0   0   0   0   0   0   0   0   0
#> V35  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V36  0  1  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V37  0  0  0  0  0  0  1  0  0   0   0   0   1   0   0   0   0   1   0   0   0
#> V38  0  0  0  0  0  0  0  0  0   1   0   0   0   0   0   0   0   0   0   0   0
#> V39  0  1  0  0  0  0  0  0  0   0   0   0   0   1   0   0   0   0   0   0   0
#> V40  0  0  0  0  1  0  0  0  0   0   0   1   0   1   0   0   0   0   1   0   0
#>     V22 V23 V24 V25 V26 V27 V28 V29 V30 V31 V32 V33 V34 V35 V36 V37 V38 V39 V40
#> V1    0   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V2    0   0   0   0   1   0   0   0   0   0   0   0   0   0   1   0   0   1   0
#> V3    0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V4    0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V5    0   0   0   0   1   0   0   1   0   0   0   0   0   0   0   0   0   0   1
#> V6    0   0   0   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0   0
#> V7    0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   1   0   0   0
#> V8    0   0   1   0   1   0   0   1   0   0   0   0   0   0   0   0   0   0   0
#> V9    0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V10   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0
#> V11   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0   0
#> V12   1   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0   0   1
#> V13   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0
#> V14   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   1
#> V15   0   0   0   0   0   1   0   1   0   0   0   0   0   0   0   0   0   0   0
#> V16   0   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V17   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V18   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0
#> V19   1   0   0   0   0   0   0   0   0   0   1   1   0   0   0   0   0   0   1
#> V20   0   0   0   0   0   0   0   0   0   0   1   1   0   0   0   0   0   0   0
#> V21   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V22   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   1   1   0
#> V23   0   1   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0   0   0
#> V24   0   0   1   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V25   0   0   1   1   0   0   0   0   0   0   0   0   0   0   0   0   0   1   1
#> V26   0   0   0   0   1   0   1   0   0   0   0   0   0   0   0   0   0   0   1
#> V27   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0   1   0
#> V28   0   0   0   0   1   0   1   0   0   0   0   0   0   0   0   0   0   0   0
#> V29   0   0   0   0   0   0   0   1   1   0   1   0   0   0   1   0   0   0   0
#> V30   0   0   0   0   0   0   0   1   1   0   1   0   0   0   0   0   0   0   0
#> V31   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0
#> V32   0   0   0   0   0   0   0   1   1   0   1   0   0   0   0   0   0   0   1
#> V33   0   1   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0   0   0
#> V34   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0   0
#> V35   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0
#> V36   0   0   0   0   0   0   0   1   0   0   0   0   0   0   1   0   0   0   0
#> V37   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0
#> V38   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0
#> V39   1   0   0   1   0   1   0   0   0   0   0   0   0   0   0   0   0   1   0
#> V40   0   0   0   1   1   0   0   0   0   0   1   0   0   0   0   0   0   0   1

## correlation parameter
aa$tau
#> [1] 1.771347
aa$ll
#> [1] 19.10515

Estimate the network based on heterogeneous one-stage model

Generate data

set.seed(1)
dd=Simulate(type="longiheter",n=n,p=p,m1=m1,m2=m2,tt=10,alpha=5,group=1)
ddata=dd$data$pre
subjects=fct_inorder(ddata$subject)
heterData=list(data=ddata)
saveRDS(heterData,file="heterOneStageData.rds")

Estimation

set.seed(1)
aa=lglasso(data=ddata,lambda = 0.01,random=TRUE,trace=T)
#> [1] "alpha estimate: 1"
#> [1] "iteration 1 precision difference: 1.478 /correlation alpha difference: 5.796"
#> [1] "alpha estimate: 6.79566343782216"
#> [1] "iteration 2 precision difference: 0.175 /correlation alpha difference: 8.679"
#> [1] "alpha estimate: 15.4751066564369"
#> [1] "iteration 3 precision difference: 0.162 /correlation alpha difference: 0.396"
#> [1] "alpha estimate: 15.8708854280835"
#> [1] "iteration 4 precision difference: 0.153 /correlation alpha difference: 1.728"
#> [1] "alpha estimate: 14.1429926220806"
#> [1] "iteration 5 precision difference: 0.146 /correlation alpha difference: 1.117"
#> [1] "alpha estimate: 13.0255602372045"
#> [1] "iteration 6 precision difference: 0.124 /correlation alpha difference: 1.197"
#> [1] "alpha estimate: 11.828987782098"
#> [1] "iteration 7 precision difference: 0.114 /correlation alpha difference: 0.954"
#> [1] "alpha estimate: 10.8746885496785"
#> [1] "iteration 8 precision difference: 0.125 /correlation alpha difference: 0.827"
#> [1] "alpha estimate: 10.0472961652831"
#> [1] "iteration 9 precision difference: 0.096 /correlation alpha difference: 0.28"
#> [1] "alpha estimate: 9.76697338267776"
#> [1] "iteration 10 precision difference: 0.067 /correlation alpha difference: 0.509"
#> [1] "alpha estimate: 9.25837524687701"
#> [1] "iteration 11 precision difference: 0.075 /correlation alpha difference: 0.536"
#> [1] "alpha estimate: 8.7227818934082"
#> [1] "iteration 12 precision difference: 0.049 /correlation alpha difference: 0.34"
#> [1] "alpha estimate: 8.38243408782067"
#> [1] "iteration 13 precision difference: 0.056 /correlation alpha difference: 0.164"
#> [1] "alpha estimate: 8.21830572200703"
#> [1] "iteration 14 precision difference: 0.06 /correlation alpha difference: 0.256"
#> [1] "alpha estimate: 7.96185581827743"
#> [1] "iteration 15 precision difference: 0.055 /correlation alpha difference: 0.175"
#> [1] "alpha estimate: 7.7871842626904"
#> [1] "iteration 16 precision difference: 0.086 /correlation alpha difference: 0.014"
#> [1] "alpha estimate: 7.80159095380885"
#> [1] "iteration 17 precision difference: 0.035 /correlation alpha difference: 0.129"
#> [1] "alpha estimate: 7.67231920715004"
#> [1] "iteration 18 precision difference: 0.052 /correlation alpha difference: 0.125"
#> [1] "alpha estimate: 7.54751314924805"
#> [1] "iteration 19 precision difference: 0.041 /correlation alpha difference: 0.11"
#> [1] "alpha estimate: 7.43722171288938"
#> [1] "iteration 20 precision difference: 0.053 /correlation alpha difference: 0.042"
#> [1] "alpha estimate: 7.47946029825347"
#> [1] "iteration 21 precision difference: 0.04 /correlation alpha difference: 0.064"
#> [1] "alpha estimate: 7.41499307521063"
#> [1] "iteration 22 precision difference: 0.036 /correlation alpha difference: 0.151"
#> [1] "alpha estimate: 7.56587119269837"
#> [1] "iteration 23 precision difference: 0.045 /correlation alpha difference: 0.029"
#> [1] "alpha estimate: 7.53717859605908"
#> [1] "iteration 24 precision difference: 0.05 /correlation alpha difference: 0.101"
#> [1] "alpha estimate: 7.4362241684775"
#> [1] "iteration 25 precision difference: 0.033 /correlation alpha difference: 0.032"
#> [1] "alpha estimate: 7.46785119158903"
#> [1] "iteration 26 precision difference: 0.031 /correlation alpha difference: 0.088"
#> [1] "alpha estimate: 7.38030410972224"
#> [1] "iteration 27 precision difference: 0.039 /correlation alpha difference: 0.032"
#> [1] "alpha estimate: 7.34858460039623"
#> [1] "iteration 28 precision difference: 0.031 /correlation alpha difference: 0.054"
#> [1] "alpha estimate: 7.40209089454052"
#> [1] "iteration 29 precision difference: 0.044 /correlation alpha difference: 0.049"
#> [1] "alpha estimate: 7.45132320379011"
#> [1] "iteration 30 precision difference: 0.036 /correlation alpha difference: 0.006"
#> Algorithm reached the maximum iteration!
saveRDS(aa,file="heterOneStageResult.rds")
## estimated network  

estimates=lapply(aa$wi$wiList,function(ll){ifelse(abs(ll)>10^(-3),1,0)})
estimates
#> list()
##  true network
dd$network
#> $pre
#>       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
#>  [1,]    1    0    0    0    0    1    0    0    0     0     0     0     0
#>  [2,]    0    1    0    0    0    0    0    0    0     0     0     0     0
#>  [3,]    0    0    1    1    0    0    0    0    0     0     1     1     0
#>  [4,]    0    0    1    1    0    0    0    0    0     0     0     0     0
#>  [5,]    0    0    0    0    1    0    0    0    0     0     0     0     0
#>  [6,]    1    0    0    0    0    1    0    0    0     0     0     1     0
#>  [7,]    0    0    0    0    0    0    1    0    0     0     0     0     0
#>  [8,]    0    0    0    0    0    0    0    1    0     1     0     0     0
#>  [9,]    0    0    0    0    0    0    0    0    1     0     1     0     0
#> [10,]    0    0    0    0    0    0    0    1    0     1     0     1     0
#> [11,]    0    0    1    0    0    0    0    0    1     0     1     1     0
#> [12,]    0    0    1    0    0    1    0    0    0     1     1     1     0
#> [13,]    0    0    0    0    0    0    0    0    0     0     0     0     1
#> [14,]    0    0    1    0    0    0    1    0    0     0     0     0     1
#> [15,]    0    0    0    0    0    0    0    0    1     0     0     0     0
#> [16,]    0    0    0    0    0    1    1    0    0     1     0     0     0
#> [17,]    0    1    0    0    0    0    0    0    0     1     0     0     0
#> [18,]    0    0    1    0    0    0    0    0    0     1     0     0     0
#> [19,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#> [20,]    0    0    0    0    0    0    0    0    0     0     1     0     0
#> [21,]    0    0    0    0    0    0    0    1    0     0     0     0     0
#> [22,]    0    0    0    0    0    0    0    0    1     0     0     0     0
#> [23,]    1    0    1    0    0    0    0    0    0     0     0     0     0
#> [24,]    0    0    1    0    1    0    0    0    0     0     0     0     0
#> [25,]    0    0    0    0    0    0    0    0    0     0     0     1     0
#> [26,]    0    0    0    0    0    0    0    1    0     1     0     1     1
#> [27,]    0    0    1    0    0    0    0    0    0     0     0     0     0
#> [28,]    0    0    0    0    0    0    0    0    1     0     1     0     0
#> [29,]    0    0    0    0    0    0    0    0    0     0     0     1     0
#> [30,]    0    0    0    0    0    0    0    0    0     0     0     0     1
#> [31,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#> [32,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#> [33,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#> [34,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#> [35,]    0    0    0    0    0    1    0    0    0     0     1     0     0
#> [36,]    0    1    0    0    0    0    0    0    0     0     0     0     0
#> [37,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#> [38,]    0    0    0    0    0    0    0    0    0     1     0     0     0
#> [39,]    0    1    0    0    0    0    0    0    0     0     0     1     0
#> [40,]    0    0    0    0    0    0    0    0    0     0     1     0     0
#>       [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25]
#>  [1,]     0     0     0     0     0     0     0     0     0     1     0     0
#>  [2,]     0     0     0     1     0     0     0     0     0     0     0     0
#>  [3,]     1     0     0     0     1     0     0     0     0     1     1     0
#>  [4,]     0     0     0     0     0     0     0     0     0     0     0     0
#>  [5,]     0     0     0     0     0     0     0     0     0     0     1     0
#>  [6,]     0     0     1     0     0     0     0     0     0     0     0     0
#>  [7,]     1     0     1     0     0     0     0     0     0     0     0     0
#>  [8,]     0     0     0     0     0     0     0     1     0     0     0     0
#>  [9,]     0     1     0     0     0     0     0     0     1     0     0     0
#> [10,]     0     0     1     1     1     0     0     0     0     0     0     0
#> [11,]     0     0     0     0     0     0     1     0     0     0     0     0
#> [12,]     0     0     0     0     0     0     0     0     0     0     0     1
#> [13,]     1     0     0     0     0     0     0     0     0     0     0     0
#> [14,]     1     0     0     0     0     0     0     0     0     0     0     0
#> [15,]     0     1     0     0     0     0     0     0     0     0     0     0
#> [16,]     0     0     1     0     0     0     0     0     0     0     0     0
#> [17,]     0     0     0     1     0     0     0     0     0     0     0     0
#> [18,]     0     0     0     0     1     0     0     0     0     0     0     0
#> [19,]     0     0     0     0     0     1     0     0     0     1     0     0
#> [20,]     0     0     0     0     0     0     1     0     0     0     0     1
#> [21,]     0     0     0     0     0     0     0     1     0     0     0     0
#> [22,]     0     0     0     0     0     0     0     0     1     0     0     0
#> [23,]     0     0     0     0     0     1     0     0     0     1     0     0
#> [24,]     0     0     0     0     0     0     0     0     0     0     1     0
#> [25,]     0     0     0     0     0     0     1     0     0     0     0     1
#> [26,]     0     1     0     0     0     0     0     0     0     0     0     0
#> [27,]     0     0     0     1     0     0     0     0     0     1     0     0
#> [28,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [29,]     0     0     0     0     0     0     0     1     0     0     0     0
#> [30,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [31,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [32,]     0     0     1     0     0     0     1     0     0     1     0     0
#> [33,]     1     0     0     0     0     0     1     0     0     0     0     0
#> [34,]     0     1     0     0     0     0     0     0     0     0     0     1
#> [35,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [36,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [37,]     0     0     1     0     0     1     0     0     0     0     0     0
#> [38,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [39,]     1     0     0     0     0     0     0     0     1     0     1     0
#> [40,]     0     0     0     0     0     0     0     0     0     0     0     1
#>       [,26] [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37]
#>  [1,]     0     0     0     0     0     0     0     0     0     0     0     0
#>  [2,]     0     0     0     0     0     0     0     0     0     0     1     0
#>  [3,]     0     1     0     0     0     0     0     0     0     0     0     0
#>  [4,]     0     0     0     0     0     0     0     0     0     0     0     0
#>  [5,]     0     0     0     0     0     0     0     0     0     0     0     0
#>  [6,]     0     0     0     0     0     0     0     0     0     1     0     0
#>  [7,]     0     0     0     0     0     0     0     0     0     0     0     0
#>  [8,]     1     0     0     0     0     0     0     0     0     0     0     0
#>  [9,]     0     0     1     0     0     0     0     0     0     0     0     0
#> [10,]     1     0     0     0     0     0     0     0     0     0     0     0
#> [11,]     0     0     1     0     0     0     0     0     0     1     0     0
#> [12,]     1     0     0     1     0     0     0     0     0     0     0     0
#> [13,]     1     0     0     0     1     0     0     0     0     0     0     0
#> [14,]     0     0     0     0     0     0     0     1     0     0     0     0
#> [15,]     1     0     0     0     0     0     0     0     1     0     0     0
#> [16,]     0     0     0     0     0     0     1     0     0     0     0     1
#> [17,]     0     1     0     0     0     0     0     0     0     0     0     0
#> [18,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [19,]     0     0     0     0     0     0     0     0     0     0     0     1
#> [20,]     0     0     0     0     0     0     1     1     0     0     0     0
#> [21,]     0     0     0     1     0     0     0     0     0     0     0     0
#> [22,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [23,]     0     1     0     0     0     0     1     0     0     0     0     0
#> [24,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [25,]     0     0     0     0     0     0     0     0     1     0     0     0
#> [26,]     1     0     1     0     0     0     0     0     0     0     0     0
#> [27,]     0     1     0     0     1     0     0     1     0     0     0     0
#> [28,]     1     0     1     0     0     0     0     0     0     0     0     0
#> [29,]     0     0     0     1     1     0     0     0     0     0     0     0
#> [30,]     0     1     0     1     1     0     0     0     0     0     0     0
#> [31,]     0     0     0     0     0     1     0     0     0     0     0     0
#> [32,]     0     0     0     0     0     0     1     0     0     0     0     0
#> [33,]     0     1     0     0     0     0     0     1     0     0     1     0
#> [34,]     0     0     0     0     0     0     0     0     1     0     0     0
#> [35,]     0     0     0     0     0     0     0     0     0     1     0     0
#> [36,]     0     0     0     0     0     0     0     1     0     0     1     0
#> [37,]     0     0     0     0     0     0     0     0     0     0     0     1
#> [38,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [39,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [40,]     0     1     0     0     0     0     1     0     0     0     0     0
#>       [,38] [,39] [,40]
#>  [1,]     0     0     0
#>  [2,]     0     1     0
#>  [3,]     0     0     0
#>  [4,]     0     0     0
#>  [5,]     0     0     0
#>  [6,]     0     0     0
#>  [7,]     0     0     0
#>  [8,]     0     0     0
#>  [9,]     0     0     0
#> [10,]     1     0     0
#> [11,]     0     0     1
#> [12,]     0     1     0
#> [13,]     0     0     0
#> [14,]     0     1     0
#> [15,]     0     0     0
#> [16,]     0     0     0
#> [17,]     0     0     0
#> [18,]     0     0     0
#> [19,]     0     0     0
#> [20,]     0     0     0
#> [21,]     0     0     0
#> [22,]     0     1     0
#> [23,]     0     0     0
#> [24,]     0     1     0
#> [25,]     0     0     1
#> [26,]     0     0     0
#> [27,]     0     0     1
#> [28,]     0     0     0
#> [29,]     0     0     0
#> [30,]     0     0     0
#> [31,]     0     0     0
#> [32,]     0     0     1
#> [33,]     0     0     0
#> [34,]     0     0     0
#> [35,]     0     0     0
#> [36,]     0     0     0
#> [37,]     0     0     0
#> [38,]     1     0     0
#> [39,]     0     1     0
#> [40,]     0     0     1
aa$ll
#> [1] 48.36001
## correlation parameter
 model <- lm(dd$tau ~ aa$tau)
plot(aa$tau,dd$tau,xlab = "estimated tau",ylab="true tau")
abline(model, col = "red", lwd = 2)

summary(model)
#> 
#> Call:
#> lm(formula = dd$tau ~ aa$tau)
#> 
#> Residuals:
#>       Min        1Q    Median        3Q       Max 
#> -0.164932 -0.018982  0.005359  0.013064  0.158432 
#> 
#> Coefficients:
#>              Estimate Std. Error t value Pr(>|t|)    
#> (Intercept) -0.012445   0.008943  -1.392    0.169    
#> aa$tau       1.573142   0.051692  30.433   <2e-16 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error: 0.04377 on 58 degrees of freedom
#> Multiple R-squared:  0.9411, Adjusted R-squared:  0.9401 
#> F-statistic: 926.2 on 1 and 58 DF,  p-value: < 2.2e-16

Two-stage model

Estimate the networks based on homogeneous two-stage model

Generate data

set.seed(1)
dd=Simulate(type="longihomo",n=n,p=p,m1=m1,m2=m2,tau=c(2,1),tt=2)
ddata=do.call(rbind,dd$data)
subjects=fct_inorder(ddata$subject)
group=c(rep(0,nrow(ddata)/2),rep(1,nrow(ddata)/2))
homoTwoStageData=list(data=ddata,group=group)
saveRDS(homoTwoStageData,file="homoTwoStageData.rds")

Estimation

set.seed(1)
aa=lglasso(data=ddata,lambda = c(0.1,0.1),group = group,trace=T)
#> [1] "iteration 1 precision difference: 0.796 /correlation tau difference: 0.337"
#> [1] "iteration 2 precision difference: 0.511 /correlation tau difference: 1.893"
#> [1] "iteration 3 precision difference: 0.511 /correlation tau difference: 1.099"
#> [1] "iteration 4 precision difference: 0.07 /correlation tau difference: 1.038"
#> [1] "iteration 5 precision difference: 0.07 /correlation tau difference: 0.225"
#> [1] "iteration 6 precision difference: 0.014 /correlation tau difference: 0.222"
#> [1] "iteration 7 precision difference: 0.014 /correlation tau difference: 0.026"
#> [1] "iteration 8 precision difference: 0.001 /correlation tau difference: 0.026"
#> [1] "iteration 9 precision difference: 0.002 /correlation tau difference: 0.003"
saveRDS(aa,file="homoTwoStageResult.rds")
estimates=lapply(aa$wi,function(ll){ifelse(abs(ll)>10^(-3),1,0)})

## pre-treatment network estimate 
estimates[[1]]
#>     V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12 V13 V14 V15 V16 V17 V18 V19 V20 V21
#> V1   1  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   1   0   0   0   0
#> V2   0  1  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V3   0  0  1  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V4   0  0  0  1  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V5   0  0  0  0  1  0  0  0  0   0   0   1   0   1   0   0   0   0   0   0   0
#> V6   0  0  0  0  0  1  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V7   0  0  0  0  0  0  1  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V8   0  0  0  0  0  0  0  1  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V9   0  0  0  0  0  0  0  0  1   0   0   0   0   0   0   0   0   0   0   0   0
#> V10  0  0  0  0  0  0  0  0  0   1   0   0   0   0   0   0   0   0   0   0   0
#> V11  0  0  0  0  0  0  0  0  0   0   1   0   0   0   0   0   0   0   0   0   0
#> V12  0  0  0  0  1  0  0  0  0   0   0   1   0   0   0   0   0   0   0   0   0
#> V13  0  0  0  0  0  0  0  0  0   0   0   0   1   0   0   0   0   0   0   0   0
#> V14  0  0  0  0  1  0  0  0  0   0   0   0   0   1   0   0   0   0   0   0   0
#> V15  0  0  0  0  0  0  0  0  0   0   0   0   0   0   1   0   0   0   0   0   0
#> V16  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   1   0   0   0   0   0
#> V17  1  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   1   0   0   0   0
#> V18  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   1   0   0   0
#> V19  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   1   0   0
#> V20  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   1   0
#> V21  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   1
#> V22  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V23  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V24  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V25  0  0  0  0  0  0  0  0  0   0   0   0   0   0   1   0   0   0   0   0   0
#> V26  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V27  0  0  0  1  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   1
#> V28  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V29  0  0  0  0  0  1  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V30  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V31  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   1
#> V32  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V33  0  0  0  1  0  0  0  0  0   0   0   0   1   0   1   0   0   0   0   0   0
#> V34  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V35  1  0  1  0  0  0  0  1  0   0   0   1   0   0   0   0   1   0   0   0   1
#> V36  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V37  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V38  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V39  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V40  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#>     V22 V23 V24 V25 V26 V27 V28 V29 V30 V31 V32 V33 V34 V35 V36 V37 V38 V39 V40
#> V1    0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0
#> V2    0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V3    0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0
#> V4    0   0   0   0   0   1   0   0   0   0   0   1   0   0   0   0   0   0   0
#> V5    0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V6    0   0   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0
#> V7    0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V8    0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0
#> V9    0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V10   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V11   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V12   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0
#> V13   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0   0   0
#> V14   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V15   0   0   0   1   0   0   0   0   0   0   0   1   0   0   0   0   0   0   0
#> V16   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V17   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0
#> V18   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V19   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V20   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V21   0   0   0   0   0   1   0   0   0   1   0   0   0   1   0   0   0   0   0
#> V22   1   0   0   0   0   0   0   0   0   0   0   1   0   1   0   0   0   0   0
#> V23   0   1   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0
#> V24   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V25   0   0   0   1   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0
#> V26   0   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V27   0   0   0   0   0   1   0   0   0   0   0   1   0   0   0   0   0   0   0
#> V28   0   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0
#> V29   0   0   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0
#> V30   0   0   0   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0   0
#> V31   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0
#> V32   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0   0   0   0
#> V33   1   0   0   0   0   1   0   0   0   0   0   1   0   0   0   0   0   0   0
#> V34   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0   0
#> V35   1   0   0   1   0   0   0   0   0   0   0   0   0   1   0   1   0   0   0
#> V36   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0
#> V37   0   1   0   0   0   0   0   0   0   0   0   0   0   1   0   1   0   0   0
#> V38   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0
#> V39   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0
#> V40   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1

##  true post-treatment network
dd$network$pre
#>     V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12 V13 V14 V15 V16 V17 V18 V19 V20 V21
#> V1   1  0  0  0  0  0  0  0  0   0   0   1   0   0   0   0   1   0   0   0   0
#> V2   0  1  1  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   1   0
#> V3   0  1  1  0  0  0  0  0  0   0   0   0   0   1   0   0   0   0   0   0   0
#> V4   0  0  0  1  0  0  0  1  0   0   1   0   0   0   0   0   0   0   0   0   0
#> V5   0  0  0  0  1  0  0  0  0   0   0   1   0   1   0   0   0   0   0   0   0
#> V6   0  0  0  0  0  1  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V7   0  0  0  0  0  0  1  0  0   0   0   0   0   0   0   0   1   0   0   0   0
#> V8   0  0  0  1  0  0  0  1  0   0   0   0   0   0   0   0   0   0   1   1   0
#> V9   0  0  0  0  0  0  0  0  1   0   0   0   0   0   0   0   0   0   0   1   0
#> V10  0  0  0  0  0  0  0  0  0   1   0   0   0   0   0   0   0   0   0   1   0
#> V11  0  0  0  1  0  0  0  0  0   0   1   0   0   0   0   0   0   0   0   0   0
#> V12  1  0  0  0  1  0  0  0  0   0   0   1   0   0   0   0   0   1   0   0   0
#> V13  0  0  0  0  0  0  0  0  0   0   0   0   1   0   1   0   1   0   0   0   0
#> V14  0  0  1  0  1  0  0  0  0   0   0   0   0   1   0   0   0   1   1   1   0
#> V15  0  0  0  0  0  0  0  0  0   0   0   0   1   0   1   0   0   0   0   0   0
#> V16  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   1   0   0   0   0   0
#> V17  1  0  0  0  0  0  1  0  0   0   0   0   1   0   0   0   1   0   0   0   0
#> V18  0  0  0  0  0  0  0  0  0   0   0   1   0   1   0   0   0   1   0   0   0
#> V19  0  0  0  0  0  0  0  1  0   0   0   0   0   1   0   0   0   0   1   0   0
#> V20  0  1  0  0  0  0  0  1  1   1   0   0   0   1   0   0   0   0   0   1   0
#> V21  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   1
#> V22  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V23  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   1   0   0   0   0   0
#> V24  0  0  0  0  0  0  1  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V25  0  0  1  0  0  0  0  0  0   0   0   0   0   0   1   0   0   0   0   0   0
#> V26  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   1   0   0   0   0   0
#> V27  0  0  0  1  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   1
#> V28  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V29  0  0  0  0  0  1  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V30  1  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V31  1  0  0  0  0  0  0  0  1   0   0   0   1   0   0   0   0   0   0   0   0
#> V32  0  0  0  0  0  1  1  0  1   0   0   0   0   0   1   0   0   0   0   0   0
#> V33  0  0  0  0  0  0  0  0  0   0   0   0   0   1   0   0   0   0   0   0   0
#> V34  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   1   0   0
#> V35  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V36  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   1   0   0   0   1   0
#> V37  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V38  0  0  0  0  0  0  1  1  1   1   0   0   0   0   0   0   0   0   0   0   0
#> V39  0  0  0  0  0  0  0  0  0   0   0   1   0   1   0   0   1   0   0   0   0
#> V40  0  0  0  1  0  0  0  0  0   0   1   0   0   0   0   0   1   0   0   0   0
#>     V22 V23 V24 V25 V26 V27 V28 V29 V30 V31 V32 V33 V34 V35 V36 V37 V38 V39 V40
#> V1    0   0   0   0   0   0   0   0   1   1   0   0   0   0   0   0   0   0   0
#> V2    0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V3    0   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V4    0   0   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0   1
#> V5    0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V6    0   0   0   0   0   0   0   1   0   0   1   0   0   0   0   0   0   0   0
#> V7    0   0   1   0   0   0   0   0   0   0   1   0   0   0   0   0   1   0   0
#> V8    0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0
#> V9    0   0   0   0   0   0   0   0   0   1   1   0   0   0   0   0   1   0   0
#> V10   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0
#> V11   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1
#> V12   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0
#> V13   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0
#> V14   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0   1   0
#> V15   0   0   0   1   0   0   0   0   0   0   1   0   0   0   0   0   0   0   0
#> V16   0   1   0   0   1   0   0   0   0   0   0   0   0   0   1   0   0   0   0
#> V17   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   1
#> V18   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V19   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0   0
#> V20   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0
#> V21   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V22   1   0   0   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0   0
#> V23   0   1   0   0   0   0   0   0   0   0   1   0   0   0   1   1   0   0   0
#> V24   0   0   1   0   1   0   1   0   0   0   0   0   0   0   0   0   0   0   1
#> V25   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V26   0   0   1   0   1   0   1   0   0   0   0   0   0   0   0   0   0   0   0
#> V27   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0   1
#> V28   0   0   1   0   1   0   1   0   1   0   1   0   0   0   0   0   0   1   0
#> V29   0   0   0   0   0   0   0   1   0   1   1   0   0   0   0   1   0   0   0
#> V30   1   0   0   0   0   0   1   0   1   0   0   0   0   0   0   0   0   1   1
#> V31   0   0   0   0   0   0   0   1   0   1   0   0   0   0   0   0   0   1   0
#> V32   0   1   0   0   0   0   1   1   0   0   1   0   0   0   0   0   0   0   0
#> V33   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0   0   0
#> V34   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0   0
#> V35   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0
#> V36   0   1   0   0   0   0   0   0   0   0   0   0   0   0   1   0   1   0   0
#> V37   0   1   0   0   0   0   0   1   0   0   0   0   0   0   0   1   0   0   0
#> V38   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   1   1   0
#> V39   0   0   0   0   0   0   1   0   1   1   0   0   0   0   0   0   1   1   0
#> V40   0   0   1   0   0   1   0   0   1   0   0   0   0   0   0   0   0   0   1
aa$ll
#> [1] 22.4274

## post-treatment network estimate 
estimates[[2]]
#>     V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12 V13 V14 V15 V16 V17 V18 V19 V20 V21
#> V1   1  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   1   0   0   0   0
#> V2   0  1  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V3   0  0  1  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V4   0  0  0  1  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V5   0  0  0  0  1  0  0  0  0   0   0   1   0   1   0   0   0   0   0   0   0
#> V6   0  0  0  0  0  1  0  0  0   0   0   0   0   0   0   0   0   0   0   0   1
#> V7   0  0  0  0  0  0  1  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V8   0  0  0  0  0  0  0  1  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V9   0  0  0  0  0  0  0  0  1   0   0   0   0   0   0   0   0   0   0   0   0
#> V10  0  0  0  0  0  0  0  0  0   1   0   0   0   0   0   0   0   0   0   0   0
#> V11  0  0  0  0  0  0  0  0  0   0   1   0   0   0   0   0   0   0   0   0   0
#> V12  0  0  0  0  1  0  0  0  0   0   0   1   0   0   0   0   0   0   0   0   0
#> V13  0  0  0  0  0  0  0  0  0   0   0   0   1   0   0   0   0   0   0   0   0
#> V14  0  0  0  0  1  0  0  0  0   0   0   0   0   1   0   0   0   0   0   0   0
#> V15  0  0  0  0  0  0  0  0  0   0   0   0   0   0   1   0   0   0   0   0   0
#> V16  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   1   0   0   0   0   0
#> V17  1  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   1   0   0   0   0
#> V18  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   1   0   0   0
#> V19  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   1   0   0
#> V20  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   1   0
#> V21  0  0  0  0  0  1  0  0  0   0   0   0   0   0   0   0   0   0   0   0   1
#> V22  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V23  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V24  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V25  0  0  0  0  0  0  0  0  0   0   0   0   0   0   1   0   0   0   0   0   0
#> V26  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V27  0  0  0  1  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   1
#> V28  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V29  0  0  0  0  0  1  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V30  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V31  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   1
#> V32  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V33  0  0  0  1  0  0  0  0  0   0   0   0   1   0   1   0   0   0   0   0   0
#> V34  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V35  1  0  1  0  0  0  1  1  0   1   0   1   1   0   0   0   1   0   0   0   1
#> V36  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V37  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V38  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V39  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V40  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#>     V22 V23 V24 V25 V26 V27 V28 V29 V30 V31 V32 V33 V34 V35 V36 V37 V38 V39 V40
#> V1    0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0
#> V2    0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V3    0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0
#> V4    0   0   0   0   0   1   0   0   0   0   0   1   0   0   0   0   0   0   0
#> V5    0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V6    0   0   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0
#> V7    0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0
#> V8    0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0
#> V9    0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V10   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0
#> V11   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V12   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0
#> V13   0   0   0   0   0   0   0   0   0   0   0   1   0   1   0   0   0   0   0
#> V14   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V15   0   0   0   1   0   0   0   0   0   0   0   1   0   0   0   0   0   0   0
#> V16   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V17   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0
#> V18   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V19   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V20   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V21   0   0   0   0   0   1   0   0   0   1   0   0   0   1   0   0   0   0   0
#> V22   1   0   0   0   0   0   0   0   0   0   0   1   0   1   0   0   0   0   0
#> V23   0   1   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0
#> V24   0   0   1   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0
#> V25   0   0   0   1   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0
#> V26   0   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V27   0   0   0   0   0   1   0   0   0   0   0   1   0   0   0   0   0   0   0
#> V28   0   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0
#> V29   0   0   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0
#> V30   0   0   0   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0   0
#> V31   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0
#> V32   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0   0   0   0
#> V33   1   0   0   0   0   1   0   0   0   0   0   1   0   1   0   0   0   0   0
#> V34   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0   0
#> V35   1   0   1   1   0   0   0   0   0   0   0   1   0   1   0   1   0   1   0
#> V36   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0
#> V37   0   1   0   0   0   0   0   0   0   0   0   0   0   1   0   1   0   0   0
#> V38   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0
#> V39   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   1   0
#> V40   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1

##  true post-treatment network
dd$network$post
#>     V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12 V13 V14 V15 V16 V17 V18 V19 V20 V21
#> V1   0  0  0  0  0  0  0  0  0   0   0   1   0   0   0   0   1   0   0   0   0
#> V2   0  0  1  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   1   0
#> V3   0  1  0  0  0  0  0  0  0   0   0   0   0   1   0   1   0   0   0   0   0
#> V4   0  0  0  0  0  0  0  1  0   0   1   0   0   0   0   0   0   0   0   0   0
#> V5   0  0  0  0  0  0  0  0  0   0   0   1   0   1   0   0   0   0   0   0   0
#> V6   0  0  0  0  0  0  0  0  0   0   1   0   0   0   0   0   0   0   0   0   0
#> V7   0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   1   0   0   0   0
#> V8   0  0  0  1  0  0  0  0  0   0   0   0   0   0   0   0   0   0   1   1   0
#> V9   0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   1   0
#> V10  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   1   0
#> V11  0  0  0  1  0  1  0  0  0   0   0   0   0   0   0   0   0   0   1   0   0
#> V12  1  0  0  0  1  0  0  0  0   0   0   0   0   0   0   0   0   1   0   0   0
#> V13  0  0  0  0  0  0  0  0  0   0   0   0   0   1   1   0   1   0   0   0   0
#> V14  0  0  1  0  1  0  0  0  0   0   0   0   1   0   0   1   0   1   1   1   0
#> V15  0  0  0  0  0  0  0  0  0   0   0   0   1   0   0   0   0   0   0   0   0
#> V16  0  0  1  0  0  0  0  0  0   0   0   0   0   1   0   0   0   0   1   0   0
#> V17  1  0  0  0  0  0  1  0  0   0   0   0   1   0   0   0   0   0   0   0   0
#> V18  0  0  0  0  0  0  0  0  0   0   0   1   0   1   0   0   0   0   0   0   0
#> V19  0  0  0  0  0  0  0  1  0   0   1   0   0   1   0   1   0   0   0   0   0
#> V20  0  1  0  0  0  0  0  1  1   1   0   0   0   1   0   0   0   0   0   0   0
#> V21  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V22  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   1   0   0
#> V23  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   1   0   0   0   0   0
#> V24  0  0  0  0  0  0  1  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V25  0  0  1  0  0  0  0  0  0   0   0   0   0   0   1   0   0   0   0   0   0
#> V26  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   1   0   0   0   0   0
#> V27  0  0  0  1  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   1
#> V28  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V29  0  0  1  0  0  1  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V30  1  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   1   0   0   0   0
#> V31  0  0  0  0  0  0  0  0  1   0   0   0   1   0   0   0   0   0   0   0   0
#> V32  0  1  0  0  0  1  1  0  1   0   0   0   0   1   1   0   0   0   0   0   0
#> V33  0  0  0  0  0  0  0  0  0   0   0   0   0   1   0   0   0   0   0   0   0
#> V34  0  1  0  0  0  0  0  0  0   0   0   0   0   0   0   1   0   0   1   0   0
#> V35  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V36  0  0  1  0  0  0  0  0  0   0   0   0   0   0   0   1   0   0   0   1   0
#> V37  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V38  0  0  0  0  0  0  1  1  1   1   0   0   0   0   0   0   0   0   0   0   0
#> V39  0  0  0  0  0  0  0  0  0   0   0   1   0   1   0   0   1   0   0   0   0
#> V40  0  0  0  1  0  0  0  0  0   0   1   0   0   0   0   0   1   1   0   0   0
#>     V22 V23 V24 V25 V26 V27 V28 V29 V30 V31 V32 V33 V34 V35 V36 V37 V38 V39 V40
#> V1    0   0   0   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0   0
#> V2    0   0   0   0   0   0   0   0   0   0   1   0   1   0   0   0   0   0   0
#> V3    0   0   0   1   0   0   0   1   0   0   0   0   0   0   1   0   0   0   0
#> V4    0   0   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0   1
#> V5    0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V6    0   0   0   0   0   0   0   1   0   0   1   0   0   0   0   0   0   0   0
#> V7    0   0   1   0   0   0   0   0   0   0   1   0   0   0   0   0   1   0   0
#> V8    0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0
#> V9    0   0   0   0   0   0   0   0   0   1   1   0   0   0   0   0   1   0   0
#> V10   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0
#> V11   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1
#> V12   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0
#> V13   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0
#> V14   0   0   0   0   0   0   0   0   0   0   1   1   0   0   0   0   0   1   0
#> V15   0   0   0   1   0   0   0   0   0   0   1   0   0   0   0   0   0   0   0
#> V16   0   1   0   0   1   0   0   0   0   0   0   0   1   0   1   0   0   0   0
#> V17   0   0   0   0   0   0   0   0   1   0   0   0   0   0   0   0   0   1   1
#> V18   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1
#> V19   1   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0   0
#> V20   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0
#> V21   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V22   0   0   0   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0   0
#> V23   0   0   0   0   0   0   0   0   0   0   1   0   0   0   1   1   0   0   0
#> V24   0   0   0   0   1   0   1   0   0   0   0   0   0   0   0   0   0   0   1
#> V25   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V26   0   0   1   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0   1
#> V27   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V28   0   0   1   0   1   0   0   0   1   0   1   0   1   0   0   0   0   1   0
#> V29   0   0   0   0   0   0   0   0   0   1   1   0   0   0   0   1   0   0   0
#> V30   1   0   0   0   0   0   1   0   0   1   0   0   0   0   0   0   0   1   1
#> V31   0   0   0   0   0   0   0   1   1   0   0   0   0   0   0   0   0   1   0
#> V32   0   1   0   0   0   0   1   1   0   0   0   0   0   0   0   0   0   0   0
#> V33   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V34   0   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0
#> V35   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V36   0   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0
#> V37   0   1   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0
#> V38   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   1   0
#> V39   0   0   0   0   0   0   1   0   1   1   0   0   0   0   0   0   1   0   0
#> V40   0   0   1   0   1   0   0   0   1   0   0   0   0   0   0   0   0   0   0
## correlation parameters
aa$tau
#> [1] 2.2277904 0.9964643

Estimate the networks based on hetergeneous two-stage model

Generate data

set.seed(1)
dd=Simulate(type="longiheter",n=n,p=p,m1=m1,m2=m2,tt=20,alpha=0.5,group=2)
ddata=do.call(rbind,dd$data)
subjects=fct_inorder(ddata$subject)
group=c(rep(0,nrow(ddata)/2),rep(1,nrow(ddata)/2))
heterTwoStageData=list(data=ddata,group=group)
saveRDS(heterTwoStageData,file="heterTwoStageData.rds")

Estimation

set.seed(1)
aa=lglasso(data=ddata,lambda = c(0.1,0.1),random=T,group = group,trace=T)
#> [1] "alpha estimate: 1"
#> [1] "iteration 1 precision difference: 0.708 /correlation alpha difference: 0.195"
#> [1] "alpha estimate: 1.19512436978389"
#> [1] "iteration 2 precision difference: 0.205 /correlation alpha difference: 0.384"
#> [1] "alpha estimate: 0.811223304176149"
#> [1] "iteration 3 precision difference: 0.066 /correlation alpha difference: 0.101"
#> [1] "alpha estimate: 0.710522890084319"
#> [1] "iteration 4 precision difference: 0.026 /correlation alpha difference: 0.021"
#> [1] "alpha estimate: 0.689553991757097"
#> [1] "iteration 5 precision difference: 0.016 /correlation alpha difference: 0.015"
#> [1] "alpha estimate: 0.675005938899547"
#> [1] "iteration 6 precision difference: 0.005 /correlation alpha difference: 0.006"
saveRDS(aa,file="heterTwoStageResult.rds")
estimates=lapply(aa$wi,function(ll){ifelse(abs(ll)>10^(-3),1,0)})

## pre-treatment network estimate 
estimates[[1]]
#>     V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12 V13 V14 V15 V16 V17 V18 V19 V20 V21
#> V1   1  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   1   0   0   0
#> V2   0  1  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V3   0  0  1  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V4   0  0  0  1  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   1
#> V5   0  0  0  0  1  0  0  0  0   1   0   0   0   0   0   0   0   0   0   0   0
#> V6   0  0  0  0  0  1  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V7   0  0  0  0  0  0  1  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V8   0  0  0  0  0  0  0  1  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V9   0  0  0  0  0  0  0  0  1   0   0   0   0   0   0   0   0   0   0   0   0
#> V10  0  0  0  0  1  0  0  0  0   1   0   0   0   0   0   0   0   0   0   0   0
#> V11  0  0  0  0  0  0  0  0  0   0   1   0   0   0   0   0   0   0   0   0   0
#> V12  0  0  0  0  0  0  0  0  0   0   0   1   0   0   0   1   0   0   0   0   0
#> V13  0  0  0  0  0  0  0  0  0   0   0   0   1   0   0   0   0   0   0   0   0
#> V14  0  0  0  0  0  0  0  0  0   0   0   0   0   1   0   0   0   0   0   0   0
#> V15  0  0  0  0  0  0  0  0  0   0   0   0   0   0   1   0   0   0   0   0   0
#> V16  0  0  0  0  0  0  0  0  0   0   0   1   0   0   0   1   0   0   0   0   0
#> V17  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   1   0   0   0   0
#> V18  1  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   1   0   0   0
#> V19  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   1   0   0
#> V20  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   1   0
#> V21  0  0  0  1  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   1
#> V22  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V23  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V24  0  0  0  0  0  0  0  0  0   0   0   0   0   1   0   0   0   0   0   0   0
#> V25  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V26  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V27  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V28  1  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V29  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V30  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V31  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V32  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V33  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V34  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V35  0  0  0  0  1  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V36  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V37  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V38  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V39  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V40  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#>     V22 V23 V24 V25 V26 V27 V28 V29 V30 V31 V32 V33 V34 V35 V36 V37 V38 V39 V40
#> V1    0   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0
#> V2    0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V3    0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V4    0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V5    0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0
#> V6    0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V7    0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V8    0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V9    0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V10   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V11   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V12   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V13   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V14   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V15   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V16   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V17   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V18   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V19   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V20   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V21   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V22   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V23   0   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V24   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V25   0   0   0   1   0   0   0   1   0   0   1   0   0   0   0   0   0   0   0
#> V26   0   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V27   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V28   0   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0   1   0   0
#> V29   0   0   0   1   0   0   0   1   0   0   1   0   0   0   0   0   0   0   0
#> V30   0   0   0   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0   0
#> V31   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0
#> V32   0   0   0   1   0   0   0   1   0   0   1   0   0   0   0   0   0   0   0
#> V33   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0   0   0
#> V34   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0   0
#> V35   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0
#> V36   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0
#> V37   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0
#> V38   0   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0   1   0   0
#> V39   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0
#> V40   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1

##  true pre-treatment network
dd$network$pre
#>       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
#>  [1,]    1    0    0    0    0    0    0    0    0     0     0     0     0
#>  [2,]    0    1    0    0    0    0    0    0    0     0     1     0     1
#>  [3,]    0    0    1    0    0    0    0    0    0     0     0     0     0
#>  [4,]    0    0    0    1    0    0    0    0    0     0     0     0     0
#>  [5,]    0    0    0    0    1    0    0    0    0     1     0     0     0
#>  [6,]    0    0    0    0    0    1    0    0    0     0     0     0     1
#>  [7,]    0    0    0    0    0    0    1    0    0     0     0     0     0
#>  [8,]    0    0    0    0    0    0    0    1    0     0     1     0     1
#>  [9,]    0    0    0    0    0    0    0    0    1     0     0     0     0
#> [10,]    0    0    0    0    1    0    0    0    0     1     0     0     0
#> [11,]    0    1    0    0    0    0    0    1    0     0     1     0     0
#> [12,]    0    0    0    0    0    0    0    0    0     0     0     1     0
#> [13,]    0    1    0    0    0    1    0    1    0     0     0     0     1
#> [14,]    0    0    1    0    0    0    0    0    0     0     0     0     0
#> [15,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#> [16,]    0    0    0    0    0    0    0    0    0     0     0     1     1
#> [17,]    0    0    0    0    0    0    0    1    0     0     0     0     0
#> [18,]    1    0    0    0    0    0    0    0    0     0     0     0     0
#> [19,]    0    0    0    0    0    0    0    0    1     0     0     0     0
#> [20,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#> [21,]    1    0    0    1    0    0    1    0    0     0     0     0     0
#> [22,]    0    0    0    0    0    0    1    0    1     1     0     0     0
#> [23,]    0    0    1    0    0    1    0    0    1     0     0     0     0
#> [24,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#> [25,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#> [26,]    0    0    0    0    0    0    0    0    1     1     0     0     0
#> [27,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#> [28,]    1    0    0    0    0    0    0    0    0     0     0     0     0
#> [29,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#> [30,]    0    1    0    0    0    0    0    0    0     0     0     0     0
#> [31,]    0    0    0    0    0    0    0    0    0     1     0     0     1
#> [32,]    0    0    0    0    0    0    1    0    0     0     0     0     1
#> [33,]    0    0    0    0    0    0    0    1    0     0     0     0     0
#> [34,]    0    1    0    0    0    0    0    0    0     0     0     0     0
#> [35,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#> [36,]    0    0    0    0    0    0    0    0    0     0     0     0     1
#> [37,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#> [38,]    0    0    1    0    0    0    0    1    0     0     0     0     0
#> [39,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#> [40,]    0    0    0    0    0    0    0    1    0     0     0     0     0
#>       [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25]
#>  [1,]     0     0     0     0     1     0     0     1     0     0     0     0
#>  [2,]     0     0     0     0     0     0     0     0     0     0     0     0
#>  [3,]     1     0     0     0     0     0     0     0     0     1     0     0
#>  [4,]     0     0     0     0     0     0     0     1     0     0     0     0
#>  [5,]     0     0     0     0     0     0     0     0     0     0     0     0
#>  [6,]     0     0     0     0     0     0     0     0     0     1     0     0
#>  [7,]     0     0     0     0     0     0     0     1     1     0     0     0
#>  [8,]     0     0     0     1     0     0     0     0     0     0     0     0
#>  [9,]     0     0     0     0     0     1     0     0     1     1     0     0
#> [10,]     0     0     0     0     0     0     0     0     1     0     0     0
#> [11,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [12,]     0     0     1     0     0     0     0     0     0     0     0     0
#> [13,]     0     0     1     0     0     0     0     0     0     0     0     0
#> [14,]     1     0     0     1     0     0     0     0     0     0     1     0
#> [15,]     0     1     1     0     0     0     0     0     0     0     0     0
#> [16,]     0     1     1     0     0     0     1     0     0     0     0     0
#> [17,]     1     0     0     1     0     0     0     0     0     0     0     0
#> [18,]     0     0     0     0     1     0     0     0     0     0     0     0
#> [19,]     0     0     0     0     0     1     0     0     0     1     0     0
#> [20,]     0     0     1     0     0     0     1     0     0     0     0     0
#> [21,]     0     0     0     0     0     0     0     1     0     0     0     0
#> [22,]     0     0     0     0     0     0     0     0     1     0     0     0
#> [23,]     0     0     0     0     0     1     0     0     0     1     0     0
#> [24,]     1     0     0     0     0     0     0     0     0     0     1     1
#> [25,]     0     0     0     0     0     0     0     0     0     0     1     1
#> [26,]     0     0     0     1     0     0     0     0     0     0     0     0
#> [27,]     0     0     1     0     0     0     0     0     0     0     0     0
#> [28,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [29,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [30,]     0     0     0     0     0     0     1     0     0     0     0     0
#> [31,]     0     0     1     0     0     0     0     0     0     0     1     0
#> [32,]     0     0     0     0     0     0     0     0     0     0     1     1
#> [33,]     0     0     1     0     0     0     0     1     0     0     0     0
#> [34,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [35,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [36,]     0     1     0     1     0     0     1     1     0     1     1     0
#> [37,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [38,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [39,]     0     1     0     0     0     0     0     0     0     0     0     0
#> [40,]     0     0     0     0     0     0     0     0     0     1     0     0
#>       [,26] [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37]
#>  [1,]     0     0     1     0     0     0     0     0     0     0     0     0
#>  [2,]     0     0     0     0     1     0     0     0     1     0     0     0
#>  [3,]     0     0     0     0     0     0     0     0     0     0     0     0
#>  [4,]     0     0     0     0     0     0     0     0     0     0     0     0
#>  [5,]     0     0     0     0     0     0     0     0     0     0     0     0
#>  [6,]     0     0     0     0     0     0     0     0     0     0     0     0
#>  [7,]     0     0     0     0     0     0     1     0     0     0     0     0
#>  [8,]     0     0     0     0     0     0     0     1     0     0     0     0
#>  [9,]     1     0     0     0     0     0     0     0     0     0     0     0
#> [10,]     1     0     0     0     0     1     0     0     0     0     0     0
#> [11,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [12,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [13,]     0     0     0     0     0     1     1     0     0     0     1     0
#> [14,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [15,]     0     0     0     0     0     0     0     0     0     0     1     0
#> [16,]     0     1     0     0     0     1     0     1     0     0     0     0
#> [17,]     1     0     0     0     0     0     0     0     0     0     1     0
#> [18,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [19,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [20,]     0     0     0     0     1     0     0     0     0     0     1     0
#> [21,]     0     0     0     0     0     0     0     1     0     0     1     0
#> [22,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [23,]     0     0     0     0     0     0     0     0     0     0     1     0
#> [24,]     0     0     0     0     0     1     1     0     0     0     1     0
#> [25,]     0     0     0     0     0     0     1     0     0     0     0     0
#> [26,]     1     0     0     0     0     0     1     0     1     0     0     1
#> [27,]     0     1     0     0     0     0     0     0     0     0     0     0
#> [28,]     0     0     1     0     0     0     0     0     0     0     0     0
#> [29,]     0     0     0     1     0     0     1     0     0     0     0     0
#> [30,]     0     0     0     0     1     0     0     0     0     0     0     0
#> [31,]     0     0     0     0     0     1     0     0     0     0     0     0
#> [32,]     1     0     0     1     0     0     1     0     0     0     0     0
#> [33,]     0     0     0     0     0     0     0     1     0     0     1     0
#> [34,]     1     0     0     0     0     0     0     0     1     0     0     1
#> [35,]     0     0     0     0     0     0     0     0     0     1     0     0
#> [36,]     0     0     0     0     0     0     0     1     0     0     1     0
#> [37,]     1     0     0     0     0     0     0     0     1     0     0     1
#> [38,]     0     0     1     0     0     0     0     0     0     0     0     1
#> [39,]     0     0     0     0     0     0     0     0     0     0     1     0
#> [40,]     0     1     0     0     0     0     0     1     1     0     0     0
#>       [,38] [,39] [,40]
#>  [1,]     0     0     0
#>  [2,]     0     0     0
#>  [3,]     1     0     0
#>  [4,]     0     0     0
#>  [5,]     0     0     0
#>  [6,]     0     0     0
#>  [7,]     0     0     0
#>  [8,]     1     0     1
#>  [9,]     0     0     0
#> [10,]     0     0     0
#> [11,]     0     0     0
#> [12,]     0     0     0
#> [13,]     0     0     0
#> [14,]     0     0     0
#> [15,]     0     1     0
#> [16,]     0     0     0
#> [17,]     0     0     0
#> [18,]     0     0     0
#> [19,]     0     0     0
#> [20,]     0     0     0
#> [21,]     0     0     0
#> [22,]     0     0     0
#> [23,]     0     0     1
#> [24,]     0     0     0
#> [25,]     0     0     0
#> [26,]     0     0     0
#> [27,]     0     0     1
#> [28,]     1     0     0
#> [29,]     0     0     0
#> [30,]     0     0     0
#> [31,]     0     0     0
#> [32,]     0     0     0
#> [33,]     0     0     1
#> [34,]     0     0     1
#> [35,]     0     0     0
#> [36,]     0     1     0
#> [37,]     1     0     0
#> [38,]     1     0     0
#> [39,]     0     1     0
#> [40,]     0     0     1

aa$ll
#> [1] 14.01754
## post-treatment network estimate 
estimates[[2]]
#>     V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12 V13 V14 V15 V16 V17 V18 V19 V20 V21
#> V1   1  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   1   0   0   0
#> V2   0  1  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V3   0  0  1  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V4   0  0  0  1  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   1
#> V5   0  0  0  0  1  0  0  0  0   1   0   0   0   0   0   0   0   0   0   0   0
#> V6   0  0  0  0  0  1  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V7   0  0  0  0  0  0  1  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V8   0  0  0  0  0  0  0  1  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V9   0  0  0  0  0  0  0  0  1   0   0   0   0   0   0   0   0   0   0   0   0
#> V10  0  0  0  0  1  0  0  0  0   1   0   0   0   0   0   0   0   0   0   0   0
#> V11  0  0  0  0  0  0  0  0  0   0   1   0   0   0   0   0   0   0   0   0   0
#> V12  0  0  0  0  0  0  0  0  0   0   0   1   0   0   0   1   0   0   0   0   0
#> V13  0  0  0  0  0  0  0  0  0   0   0   0   1   0   0   0   0   0   0   0   0
#> V14  0  0  0  0  0  0  0  0  0   0   0   0   0   1   0   0   0   0   0   0   0
#> V15  0  0  0  0  0  0  0  0  0   0   0   0   0   0   1   0   0   0   0   0   0
#> V16  0  0  0  0  0  0  0  0  0   0   0   1   0   0   0   1   0   0   0   0   0
#> V17  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   1   0   0   0   0
#> V18  1  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   1   0   0   0
#> V19  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   1   0   0
#> V20  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   1   0
#> V21  0  0  0  1  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   1
#> V22  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V23  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V24  0  0  0  0  0  0  0  0  0   0   0   0   0   1   0   0   0   0   0   0   0
#> V25  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V26  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V27  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V28  1  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V29  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V30  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V31  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V32  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V33  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V34  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V35  0  0  0  0  1  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V36  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V37  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V38  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V39  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#> V40  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0
#>     V22 V23 V24 V25 V26 V27 V28 V29 V30 V31 V32 V33 V34 V35 V36 V37 V38 V39 V40
#> V1    0   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0
#> V2    0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V3    0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V4    0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V5    0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0
#> V6    0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V7    0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V8    0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V9    0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V10   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V11   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V12   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V13   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V14   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V15   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V16   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V17   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V18   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V19   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V20   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V21   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V22   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V23   0   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V24   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V25   0   0   0   1   0   0   0   1   0   0   1   0   0   1   0   0   0   0   0
#> V26   0   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V27   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0   0
#> V28   0   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0   1   0   0
#> V29   0   0   0   1   0   0   0   1   0   0   1   0   0   0   0   0   0   0   0
#> V30   0   0   0   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0   0
#> V31   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0
#> V32   0   0   0   1   0   0   0   1   0   0   1   0   0   0   0   0   0   0   0
#> V33   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0   0   0
#> V34   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0   0
#> V35   0   0   0   1   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0
#> V36   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0
#> V37   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0
#> V38   0   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0   1   0   0
#> V39   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0
#> V40   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1

##  true post-treatment network
dd$network$post
#>       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
#>  [1,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#>  [2,]    0    0    0    0    0    0    0    1    0     0     1     0     1
#>  [3,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#>  [4,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#>  [5,]    0    0    0    0    0    0    0    0    0     1     0     0     0
#>  [6,]    0    0    0    0    0    0    0    0    0     0     0     0     1
#>  [7,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#>  [8,]    0    1    0    0    0    0    0    0    0     0     1     0     1
#>  [9,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#> [10,]    0    0    0    0    1    0    0    0    0     0     0     0     0
#> [11,]    0    1    0    0    0    0    0    1    0     0     0     0     0
#> [12,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#> [13,]    0    1    0    0    0    1    0    1    0     0     0     0     0
#> [14,]    0    0    1    0    0    0    0    0    0     0     0     0     0
#> [15,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#> [16,]    0    0    0    0    0    0    0    0    0     0     0     1     1
#> [17,]    0    0    0    0    0    0    0    1    0     0     0     0     0
#> [18,]    1    0    1    0    0    0    0    0    0     0     0     0     0
#> [19,]    0    0    0    0    0    0    0    0    1     1     0     0     0
#> [20,]    0    0    1    0    0    0    0    0    0     0     1     0     0
#> [21,]    0    0    0    1    0    0    1    0    0     0     0     0     0
#> [22,]    0    0    0    0    0    0    1    1    1     1     0     0     0
#> [23,]    0    0    1    0    0    1    0    0    0     0     0     0     0
#> [24,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#> [25,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#> [26,]    0    0    0    0    0    0    0    0    1     1     0     0     0
#> [27,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#> [28,]    1    0    0    0    0    0    0    0    0     0     0     0     0
#> [29,]    0    0    0    0    0    0    0    0    1     0     0     0     0
#> [30,]    0    1    0    0    0    0    0    0    0     0     0     0     0
#> [31,]    0    0    0    0    0    0    0    0    0     1     0     0     1
#> [32,]    0    0    0    0    0    0    1    0    0     0     0     0     1
#> [33,]    0    0    0    0    0    0    0    1    0     0     0     0     0
#> [34,]    0    1    0    0    0    1    0    0    0     0     0     0     0
#> [35,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#> [36,]    0    0    0    0    0    0    0    0    0     0     0     0     1
#> [37,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#> [38,]    0    0    1    0    0    0    0    1    0     0     0     0     0
#> [39,]    0    0    0    0    0    0    0    0    0     0     0     0     0
#> [40,]    0    0    0    0    0    0    0    1    0     0     0     0     0
#>       [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25]
#>  [1,]     0     0     0     0     1     0     0     0     0     0     0     0
#>  [2,]     0     0     0     0     0     0     0     0     0     0     0     0
#>  [3,]     1     0     0     0     1     0     1     0     0     1     0     0
#>  [4,]     0     0     0     0     0     0     0     1     0     0     0     0
#>  [5,]     0     0     0     0     0     0     0     0     0     0     0     0
#>  [6,]     0     0     0     0     0     0     0     0     0     1     0     0
#>  [7,]     0     0     0     0     0     0     0     1     1     0     0     0
#>  [8,]     0     0     0     1     0     0     0     0     1     0     0     0
#>  [9,]     0     0     0     0     0     1     0     0     1     0     0     0
#> [10,]     0     0     0     0     0     1     0     0     1     0     0     0
#> [11,]     0     0     0     0     0     0     1     0     0     0     0     0
#> [12,]     0     0     1     0     0     0     0     0     0     0     0     0
#> [13,]     0     0     1     0     0     0     0     0     0     0     0     0
#> [14,]     0     0     0     1     0     0     0     0     0     0     1     0
#> [15,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [16,]     0     0     0     1     0     0     1     0     0     0     0     0
#> [17,]     1     0     1     0     0     0     0     0     0     0     0     0
#> [18,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [19,]     0     0     0     0     0     0     1     0     0     1     0     0
#> [20,]     0     0     1     0     0     1     0     0     0     0     0     0
#> [21,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [22,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [23,]     0     0     0     0     0     1     0     0     0     0     0     0
#> [24,]     1     0     0     0     0     0     0     0     0     0     0     1
#> [25,]     0     0     0     0     0     0     0     0     0     0     1     0
#> [26,]     0     0     0     1     0     0     0     0     0     0     0     0
#> [27,]     0     0     1     0     0     0     0     0     0     0     0     0
#> [28,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [29,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [30,]     0     0     0     0     0     0     1     0     0     0     0     0
#> [31,]     0     0     0     0     0     0     0     0     0     0     1     0
#> [32,]     0     0     0     0     1     0     0     0     0     0     1     1
#> [33,]     0     0     1     0     0     0     0     1     0     0     0     0
#> [34,]     0     0     0     0     0     1     0     0     0     0     0     1
#> [35,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [36,]     0     1     0     1     0     0     1     1     0     1     1     0
#> [37,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [38,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [39,]     0     1     0     0     0     0     0     0     0     0     0     0
#> [40,]     0     1     0     1     0     0     0     0     0     1     0     0
#>       [,26] [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37]
#>  [1,]     0     0     1     0     0     0     0     0     0     0     0     0
#>  [2,]     0     0     0     0     1     0     0     0     1     0     0     0
#>  [3,]     0     0     0     0     0     0     0     0     0     0     0     0
#>  [4,]     0     0     0     0     0     0     0     0     0     0     0     0
#>  [5,]     0     0     0     0     0     0     0     0     0     0     0     0
#>  [6,]     0     0     0     0     0     0     0     0     1     0     0     0
#>  [7,]     0     0     0     0     0     0     1     0     0     0     0     0
#>  [8,]     0     0     0     0     0     0     0     1     0     0     0     0
#>  [9,]     1     0     0     1     0     0     0     0     0     0     0     0
#> [10,]     1     0     0     0     0     1     0     0     0     0     0     0
#> [11,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [12,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [13,]     0     0     0     0     0     1     1     0     0     0     1     0
#> [14,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [15,]     0     0     0     0     0     0     0     0     0     0     1     0
#> [16,]     0     1     0     0     0     0     0     1     0     0     0     0
#> [17,]     1     0     0     0     0     0     0     0     0     0     1     0
#> [18,]     0     0     0     0     0     0     1     0     0     0     0     0
#> [19,]     0     0     0     0     0     0     0     0     1     0     0     0
#> [20,]     0     0     0     0     1     0     0     0     0     0     1     0
#> [21,]     0     0     0     0     0     0     0     1     0     0     1     0
#> [22,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [23,]     0     0     0     0     0     0     0     0     0     0     1     0
#> [24,]     0     0     0     0     0     1     1     0     0     0     1     0
#> [25,]     0     0     0     0     0     0     1     0     1     0     0     0
#> [26,]     0     0     0     0     0     0     1     0     1     0     1     1
#> [27,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [28,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [29,]     0     0     0     0     0     0     1     0     0     0     0     0
#> [30,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [31,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [32,]     1     0     0     1     0     0     0     0     0     0     0     0
#> [33,]     0     0     0     0     0     0     0     0     0     0     1     0
#> [34,]     1     0     0     0     0     0     0     0     0     0     0     1
#> [35,]     0     0     0     0     0     0     0     0     0     0     0     0
#> [36,]     1     0     0     0     0     0     0     1     0     0     0     0
#> [37,]     1     0     0     0     0     0     0     0     1     0     0     0
#> [38,]     0     0     1     0     0     0     0     0     0     0     0     1
#> [39,]     0     0     0     0     0     0     0     0     0     0     1     0
#> [40,]     0     1     0     0     0     0     0     1     1     0     0     0
#>       [,38] [,39] [,40]
#>  [1,]     0     0     0
#>  [2,]     0     0     0
#>  [3,]     1     0     0
#>  [4,]     0     0     0
#>  [5,]     0     0     0
#>  [6,]     0     0     0
#>  [7,]     0     0     0
#>  [8,]     1     0     1
#>  [9,]     0     0     0
#> [10,]     0     0     0
#> [11,]     0     0     0
#> [12,]     0     0     0
#> [13,]     0     0     0
#> [14,]     0     0     0
#> [15,]     0     1     1
#> [16,]     0     0     0
#> [17,]     0     0     1
#> [18,]     0     0     0
#> [19,]     0     0     0
#> [20,]     0     0     0
#> [21,]     0     0     0
#> [22,]     0     0     0
#> [23,]     0     0     1
#> [24,]     0     0     0
#> [25,]     0     0     0
#> [26,]     0     0     0
#> [27,]     0     0     1
#> [28,]     1     0     0
#> [29,]     0     0     0
#> [30,]     0     0     0
#> [31,]     0     0     0
#> [32,]     0     0     0
#> [33,]     0     0     1
#> [34,]     0     0     1
#> [35,]     0     0     0
#> [36,]     0     1     0
#> [37,]     1     0     0
#> [38,]     0     0     0
#> [39,]     0     0     0
#> [40,]     0     0     0

## correlation parameters
 model <- lm(dd$tau ~ aa$tau)
plot(aa$tau,dd$tau,xlab = "estimated tau",ylab="true tau")
abline(model, col = "red", lwd = 2)

summary(model)$coef
#>              Estimate Std. Error   t value     Pr(>|t|)
#> (Intercept) 0.2000971 0.11422710  1.751748 8.510324e-02
#> aa$tau      1.1940919 0.05579853 21.400061 3.287149e-29